I want to go to swim语法不对。

去做某事常用go doing结构，这是一种固定习惯用法。例如：go swimminggo skatinginggo boatinggo fishinggo huntinggo hikinggo campinggo climbinggo shopping……例句：I often go swimmimg in summer.We will go camping next Sunday.Mary went shopping after work yesterday.……

对的，但一般我们会说 I want to go swimming.

这个语法是对的，表示想要去游泳的意思，want的用法是wanttodosth，表示想要去做某事。